In a tweet, he said the move was intended to “force MPs to choose between her bad deal and a disastrous no deal”.

Labour, he said, would “work with MPs across the Commons to prevent no deal, break the deadlock and build support for our alternative plan”.

On the plane to Sharm el-Sheikh for a summit between EU and Arab league leaders, Mrs May said her team would be returning to the Belgian capital on Tuesday for further talks.

“As a result of that, we won’t bring a meaningful vote to Parliament this week, but we will ensure that that happens by 12 March,” she added.

Mrs May has already met European Council President Donald Tusk for talks after landing in Egypt and will meet other EU leaders on the fringes of the summit later.

She said negotiations were continuing over the backstop – the controversial policy that aims to prevent a hard border returning to the island of Ireland – after Parliament voted for her to seek “alternative arrangements” to what is set out in her deal.

What does 12 March Brexit vote date tell us?

It’s true that playing for time is a powerful, if cynical, political strategy and the Labour Party – and lots of Conservatives too – are annoyed that Downing Street seems to be dragging its feet like this and won’t give MPs a formal thumbs up or thumbs down vote for more than another fortnight.

The prime minister naming the next vote day might do a little to calm the tempers of those in government who have been very publicly suggesting that strategy is madness. 12 March is at least, for them, before the next EU summit.

It is not, as these things go, the final, final, moment. Reckless, many will suggest, but not a total kamikaze mission.

But it won’t stop the senior MPs Yvette Cooper and Oliver Letwin, still pushing for a vote next week for their own bill that would force the government to delay Brexit if they don’t have a deal in place by… guess when? 13 March. Oh look – the day AFTER Number 10’s new deadline.

Here, the date of 12 March suggests that the government is, as one source suggested, “planning for every eventuality”.

In other words – they think it’s likely MPs might indeed vote this week to extend the process if a deal hasn’t been done.

Mrs May also rejected an accusation – made last week by MP Anna Soubry as she quit the Conservative Party – that she had a “personal problem” with immigration.

“I have consistently said that immigration has been good for this country,” the prime minister said, adding: “It’s important that we have welcomed people coming to the country over the years – both people migrating to the UK for work purposes but also crucially those many refugees and asylum seekers.”

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Media captionAnna Soubry tells Newsnight’s Kirsty Wark she was ‘worried’ the prime minister had a problem with immigration.

And she also made clear that she wants to stay on in Number 10 after the first phase of Brexit finishes, despite having promised her MPs she would not fight the next election.

She said her job “is not just about delivering Brexit” and “there is still a domestic agenda that I want to get on with.”

‘Unbelievable’

Yvette Cooper called the latest delay “utterly shambolic”, tweeting: “Each time we get closer to cliff edge. How are businesses, public services and families supposed to plan in this chaos?”

The SNP’s Westminster leader, Ian Blackford, also called the delay “unacceptable”.

And the director general of the British Chambers of Commerce, Adam Marshall, said it was “unbelievable” to leave the vote so close to the planned exit date.

What votes are happening this week?

On Wednesday, MPs will get another chance to put forward a range of amendments to show what direction they want Brexit to take.

Top of the list is the Cooper-Letwin amendment – and cabinet ministers Greg Clark, Amber Rudd and David Gauke wrote in the Daily Mail that they would be forced to back it if the pro-Leave European Research Group (ERG) – made up of Tory backbenchers – stood in the way of the withdrawal deal being agreed “in the next few days”.

The ERG would then have “no-one to blame but themselves for delaying Brexit,” the trio said.

Environment Secretary Michael Gove has urged his cabinet colleagues against backing the Cooper-Letwin amendment, calling for “unity” behind the PM.

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Media captionGove: “I will do everything I can to persuade colleagues to stay in government.”

Labour is also likely to table an amendment on Wednesday, putting its own Brexit plan – one which backs a permanent customs union with the EU and a close relationship with its single market – to MPs.

While it’s likely to be rejected, the moment could still be significant. The party’s conference last September bound the leadership to explore all remaining alternatives to the PM’s Brexit plan, including a public vote, if it wasn’t able to force a general election.

Efforts to get an election have failed, so if Labour’s own Brexit plan is defeated in the Commons, the only remaining option would be a new referendum.

Labour’s deputy leader Tom Watson told the BBC’s Andrew Marr programme that “we are heading in that direction”, but “there is still more play in the days ahead”.

Mr Watson said the leadership was also looking at an amendment drawn up by two backbenchers, Peter Kyle and Phil Wilson, which would be tabled whenever the next meaningful vote is held.

Under the terms of that amendment, Labour MPs would support the prime minister’s Brexit deal in exchange for it then being put to a public vote.

‘Reassurance’

He accused the UK government of wanting to change the backstop to “placate a group in the Conservative Party who are insisting on moving the prime minister away from her own policies”, and reiterated that the EU would not re-open the withdrawal agreement.

But he told Sky News they would try to “provide reassurance and clarification for the British Parliament to allow them to ratify this deal”.

Speaking from the summit on Sunday, Austria’s Chancellor Sebastian Kurz said it “would be good to postpone Brexit” if the deal was not agreed by the beginning of March.